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We present the new method to calculate the critical temperature as a functionof $\Delta$, conformal dimension of the cooper operator. We find that, in theregime $1/2\leq \Delta <1$ where the AC conductivity does not show a gap, thecritical temperature is not well defined. We also got expression of ACconductivity for $\Delta=2$, which agrees with numerical result in the probeapproximation.

Heun's equation and analytic structure of the Gap in Holographic superconductivity